In many cases, the topological invariant is also observable through quantized bulk responses with associated boundary phenomena at the open end of the material. The most known example of such a response is the quantum Hall effect: a 2D electron gas in the presence of a perpendicular magnetic field exhibits a quantized transverse (Hall) conductance, where the quantization originates from topological invariants (Chern numbers) associated with the system's bandstructure [1]}, [2]}, [3]}. In correspondence to the quantized bulk response, chiral edge modes appear at the boundary of the system [4]}, [5]}, [6]}, [7]}, [8]}, [9]}. Note that the non-locality of the topological invariants implies a robustness to perturbations such as disorder - a fact that promoted the quantum Hall effect as a standard for metrology [10]}.
